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Now, what's important to remember is, almost all protoss ground units come with 1 base armour (everything except probes, high templar, and archons). Since air units don't benefit from ground armour upgrades, archons only benefit from it on 10 of their 360 s/hp, and probes probably don't bear considering, we can pretty much consider "protoss ground armour" to upgrade base armours of 1. Meanwhile, the plasma shields upgrade will always upgrade base armours of 0. So as a tendancy, the shield upgrades will be more effective than the armour upgrades on their respective point pools.
This is wrong. The percentage of damage reduction--armor/shield upgrades, guardian shield--increases by every point outstripping attack upgrades rather than decreases.
For example, a Zealot with no upgrades taking fire from Marines will take 6 damage a shot to shield and 5 to health.
If the Zealot gets 1/1 shield and armor upgrades, then the damage it takes to shields will be reduced by 1 out of 6, or 17%. The damage it takes to health will be reduced by 1 out of 5, or 20%.
This gets much more extreme the higher you go. With Guardian shield up, a Zealot with no upgrades take 4 damage to shields and 3 to health. Getting a shield upgrade on top of that reduces damage taken to shield by 1 out of 4, or 25%. But an armor upgrade reduces damage by 1 out of 3, or 33%. And if you're ahead on upgrades vs. their attack upgrades, getting further ahead will be hugely more effective. Say you have 1 armor upgrade vs. 0 attack marines, plus Guardian shield. So you're taking 4 damage a shot to shields, and 2 damage a shot to armor. Which is better to get, +1 shields or +2 armor? Well as we've established, +1 shields will reduce damage to shields in this case by 1 out of 4, or 25%. But getting your armor upgrades to +2, will reduce damage to health by 1 out of 2, or 50%. In other words, in this case +2 armor is twice as good as +1 shields--and thats ignoring that you'll have more health than shields as a rule.
Basically, reducing 5 damage to 4 is always going to be better than reducing 6 damage to 5, and the more you outstrip their damage the better this gets.
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awesomoecalypse: I think you misunderstood the arguement. You're correct that if you have a 1/1/0 stalker, going from 2 to 3 armour on 80 hit points will cause a greater increase on hits-to-kill than going from 0 to 1 shield armour on 80 shield points... when you're dealing only with direct attacks, and those direct attacks have high enough base damage to always benefit from the full armour reduction.
Part of what I'm saying is that a mutalisk's glaive wurm hits (which it causes twice as many of as primary hits), in going from 2 to 3 armour, typically experience no change at all in 25% of cases, and between zero and less than full effect in the other 75% of cases. Reducing 1 damage to 0.5 damage is *always* better than reducing 0.5 damage to 0.5 damage. To use your phrasing, it's infinite-times as good.
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Excellent analysis and very well written. I think there's clear evidence put forth by Jumai to show that if you're having trouble versus mutalisks in PvZ you're clearly better off with armor and then shields as upgrades. That being said, how often are you straight up fighting mutalisks? Generally the problem isn't dying to mutalisks in a battle, it's that you can't effectively fight them straight up, and attacking the Zerg tends to force a base-race scenario which a lot of players find less than ideal.
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On November 13 2011 01:28 lololol wrote:
Your comparison is flawed.
For example: reducing damage from 3 to 2 is not the same as reducing it from to 2 to 1, both reduce damage by 1, but the second doubles the effective durability, while the first increases it by 50%, only half of the effect.
In a direct engagement armor is better than shields, since most toss units already have 1 base armor and in small engagements the bounce damage is mostly absorbed by shields, which will regenerate anyway no matter if you have shield or armor upgrades, so the effect of the bounces will be minimal.
I've been a fan since bw
please keep posting
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On November 13 2011 11:08 Salv wrote:
Excellent analysis and very well written. I think there's clear evidence put forth by Jumai to show that if you're having trouble versus mutalisks in PvZ you're clearly better off with armor and then shields as upgrades. That being said, how often are you straight up fighting mutalisks? Generally the problem isn't dying to mutalisks in a battle, it's that you can't effectively fight them straight up, and attacking the Zerg tends to force a base-race scenario which a lot of players find less than ideal.
I agree with this somewhat, as the mutalisks tend to shy away from direct confrontations. But eventually it will get to a point (I always feel like it does) where the Protoss has no choice but to move out in a big push, and then the mutalisks and lings will be forced to engage the army, in which case the armor + shield upgrades are more beneficial to them.
Though it sometimes becomes an issue when the mutalisk numbers really start to get out of control and the splash is doing ludicrous amounts of damage, and I think that that is what this post is aiming at for the most part (basically how to help deal with heavy heavy numbers of mutalisks when that engagement occurs).
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I think what's being neglected here is that by the time protoss is considering +2 armor vs +1 shields, zerg is finishing up with +1 mutalisk attack.
How does this impact the 'glaive worm 0.5 dmg on last bounce' thing?
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Keilah: 0.5 damage appears to be the flat minimum damage an attack can do after armour reduction. Upgrades to damage increase the base damage of the attack; the "new" base damage then interacts normally with armour. My final table actually gave comparisons for all possible muta upgrade levels, but looking back, only for comparing the differences and not the actual values. For clarity:
A mutalisk with +1 hits for the base values 10, 3.33 and 1.11.
Having 1 armour reduces damage inflicted to 9, 2.33, and 0.5 respectively.
Having 2 armour (or guardian shield) reduces it to 8, 1.33, 0.5.
Having 3 armour (or 1 + guardian shield) gives 7, 0.5, 0.5.
CrAzEdMiKe and Salv: I'm not trying to imply anything about how P should play against mutalisk in a tactical or strategic sense. All I'm suggesting is that if you're *already* playing against mutalisk and *already* about to click the +2 armour upgrade, you should seriously consider clicking +1 shields instead. I'd prefer not to clutter my arguement with my playstyle preferences; I'm simply presenting a mathematical reality for other players to be aware of. I'm confident other players can apply that awareness (and ignore my opinions) on their own 
That being said, in a straght up base race, +1 shields is still doing more for you than +2 armour. So (again, in the event you're getting a second armour upgrade,) I'd still suggest prioritizing +1 shields over +2 armour.
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Interesting analysis, though I think that regardless of the related math the effectiveness depends on your unit composition. Since you speak of muta harass, though, I think you swayed me into choosing +1 shields over +1 armor when I have stalkers out, since I will also be relying on cannons to help out and they will benefit as well. In my opinion, what seems to be a crucial number is how much total reduction was done off of muta attacks over the course of the entire game. In most cases I would argue then that shields would be a better choice since there are more opportunities for shields to reduce damage done by mutas than for armor to reduce muta damage. I think that's the most relevant point in the issue, although I still am quite certain +1 attack trumps both shields and armor in pretty much every FFE situation you are in.
However, the question then becomes, is getting +1 shields a good reaction to scouting or being shown mutalisks? I don't think so. I think +1 shields is a decision that requires more thought than "I see muta so I get +1 shields," and that's where the problem lies. If +1 shields is a good thing to have vs mutas, when do I get it? Can I buy myself 140 total seconds of time so I can get shields vs mutas? Would I do that over, say, an opportunity to research blink? Am I willing or is it smart to spend 4 chronoboosts on the shield upgrade over other things? Will I be S.O.L. after getting shields if he only made 8 mutas and then continued to build up a core of roaches? Overall, there are many more important considerations for the Protoss player in PvZ before mutas ever become a factor to warrant the discussion of "+1 armor vs. +1 shields." A prominent consideration is the roach, and then how to counter the roach, and then is knowing what assists in countering the roach. Since mutas are poor in straight up fights, they are rarely seen as parts of core armies (a muta/ling army is based more on the strength of Zergs economy as opposed to actual unit strengths). In any matchup, your goal is to build an army worthy of contesting the opponents core army. Since the muta can never be a core unit of the composition, even +1 armor becomes more relevant because it assists immortals more than shield upgrades and breaks even with stalkers and sentries. In the event zealots are involved, which they are about 99% of the time, armor is still more relevant.
My conclusion therefore is that because of the importance of +1 attack, going shields or armor in PvZ will always be, at least for me, something you just do to keep pace with the game and not to fall behind. Even in situations with stalkers, cannons, and mutalisks, +1 shields, while a mathematically pertinent option, is not an option that has much in-game value, and therefore is not a relevant factor in making the decision to go armor or shield first.
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a perfect example of people that have not the slightest clue what they are talking about posting in a Forum to inform others...
Protoss shields is better because you get from 0 to 1 instead of getting from 1 to 2 is what made my day.
Yes, I mean to be harsh. If you don't understand something don't post here where others believe you.
Thank you.
OT, I started getting shield Upgrades more often, I really like them since I go Chargelot(mostly harras) and Archons as late game composition and in the mid game I have Blink Stalkers against Mutas or to harras. So your thread was perfect to improve my gameplay slightly.
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Protoss Shields (S)
Upgrades the shields of all Protoss units and structures.
Quite good too vs mutaling 
gogo double forge shield/armor *o*
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On November 16 2011 06:47 rEalGuapo wrote:
a perfect example of people that have not the slightest clue what they are talking about posting in a Forum to inform others...
Protoss shields is better because you get from 0 to 1 instead of getting from 1 to 2 is what made my day.
Yes, I mean to be harsh. If you don't understand something don't post here where others believe you.
Thank you.
OT, I started getting shield Upgrades more often, I really like them since I go Chargelot(mostly harras) and Archons as late game composition and in the mid game I have Blink Stalkers against Mutas or to harras. So your thread was perfect to improve my gameplay slightly.
Wouldn't armor be more relevant since you have maaaaaany more zealots than you do archons?
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We did the same muta / armor calculation in beta. You are right about internal fractions, and the minimum 0.5 value. Basically the conclusion was that higher armor upgrades are less worth. But I don't remember reaching the conclusion about shields before armor, interesting. Shields also have the benefit of providing their armor factor while the shield is still up - thus delaying the attack further, and allowing more options for shield regeneration without significant hp damage. I'll try it out with P, thanks.
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On November 16 2011 06:58 tehemperorer wrote:Show nested quote +On November 16 2011 06:47 rEalGuapo wrote:
a perfect example of people that have not the slightest clue what they are talking about posting in a Forum to inform others...
Protoss shields is better because you get from 0 to 1 instead of getting from 1 to 2 is what made my day.
Yes, I mean to be harsh. If you don't understand something don't post here where others believe you.
Thank you.
OT, I started getting shield Upgrades more often, I really like them since I go Chargelot(mostly harras) and Archons as late game composition and in the mid game I have Blink Stalkers against Mutas or to harras. So your thread was perfect to improve my gameplay slightly. Wouldn't armor be more relevant since you have maaaaaany more zealots than you do archons?
I use my Zealots mostly to harras via war prism, sending them to death mostly, so I try to make him lose Minerals and Gas (killing drones, tech whatever) by only using Minerals. Therefore my army consists of many an Archon, my Zealots are only good to come from a side or the back to block movement.
Plus in 200/200 fights Zealots are almost worthless against a Zerg that doesn't go mass Ling+X
So not really.
Most of the time I still get 3 Attack 3 Armor and like 2 Shield at the end -.-
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It depends on the situation as well. If you have some stalkers that took about 100 damage, having shield upgrade would decrease the amount of real damage the stalkers took, since they would benefit from an upgrade for the first 80 damage but not the last 20. If, however, the stalkers were to take 150 damage, most likely armor upgrades would have been better, unless the stalkers were hit by very hard-hitting attacks.
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hi rEalGuapo: actually I'm aware that there are increasing returns on linear mitigation when calculating shots-to-kill per target (as I'd imagine are most of the other participants). However, a target benefitting from these increased returns can still require fewer shots to kill than a target which instead begins with higher current hp.
Reducing damage done on the bounces leads to future targets coming under fire with more current hp. Going from 0 to 1 is better than going from 1 to 2 at mitigating the second bounce because the benefit from armour against this attack hardcaps at 1 armour. Going from 0 to 1 with guardian shield available similarly outperforms going from 1 to 2 due to hardcapping. Though it's a somewhat fuzzier claim, the likelyhood of striking shields vs striking hull with bounce damage is very probably in favour of striking shields.
There are opposing effects at play. The compound effect of armour stacking increases the number of attacks per single target with full hit points. The flat reduction in distributed damage accumulated when using the shield upgrade increases the number of shield points available to each new target. The relative strength of these effects is partly dependent on micro (which is why I haven't given numbers), but the value of the flat reduction increases with each target the mutas kill.
In the sample numbers I ran, if the mutas focus fire their first bounce target after a kill (ie hit the worst-hurt one), +1 shields was never more than 1 worse on shots-to-kill for the first target, never worse than 1 better for the second and subsequent targets, and always pulled ahead steadily in terms of total-shots-to-kill-x-targets.
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I might be wrong here... but don't all attacks always do at least 1 damage?
I seem to remember this from an ultralisk vs marine standpoint. If you have a fully armor-upgraded ultra, it has 6 armor. Against a basic marine with no attack upgrades, the marine can still damage the ultra (though you would think that 6 damage - 6 armor = 0 damage).
Am I wrong on this? This entire thread seems to be theory-crafting... has anybody tried this?
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On November 16 2011 07:44 TheSambassador wrote:
I might be wrong here... but don't all attacks always do at least 1 damage?
I seem to remember this from an ultralisk vs marine standpoint. If you have a fully armor-upgraded ultra, it has 6 armor. Against a basic marine with no attack upgrades, the marine can still damage the ultra (though you would think that 6 damage - 6 armor = 0 damage).
Am I wrong on this? This entire thread seems to be theory-crafting... has anybody tried this?
While it is true that no unit can ever make no dmg at all, it's not exactly true that every attack does 1dmg at least. If a unit would do 0 dmg to another unit or structure by doing the maths from dmg/armor it will start of with doing 0 dmg for the first hit, then doing 1 dmg for the second hit, again 0 dmg for the 3rd hit etc resulting in doing 0.5dmg each hit on average.
Regarding mutas:
Many people seem also theorycrafting here in this thread without actually having run precise tests or having at least a really reliable source beforehand. A muta does 9/3/1dmg without any ugprades. Each attack upgrade gives them +1/+0.33/+0.11 dmg respectively. This really means that mutas with +1 attack do 10/3.33/1.11 dmg. Here it's the same thing like above. The first glaive bounce will do 3 dmg for the first hit, 3 dmg for the second hit and 4 dmg for the third hit (after that the same thing again over and over again ...). The second glaive bounce will start of by doing 1 dmg a hit 8 times in a row and then doing 2 dmg once, after that doing 8 times 1 dmg ...
To calculate the actual dmg dealt by mutas it's now quite straightforward like with any other units: You take the base dmg of mutas with their respective upgrade level (for example 10dmg a hit with +1 attack), subtract the armor value/shield level from the unit it is hitting and if it also under the effect of a guardian shield, subtract -2 again. Now if this resulting value is below one just apply the rules I mentioned above (so for example 0.5dmg means hitting for 0, then for 1, then for 0, then for 1, ...). For the first and second bounce you need to do the same calculation. By doing this you can calculate the amount of dps (by dividing the dmg dealt with each shot with the refire rate of the unit) and can do comparisions of your own about how effective other units like stalkers/sentries etc are vs them in a straight up fight and check how much difference the upgrades are doing.
I advice that you always do calculations with both glaive bounce attacks included and once without if you compare different upgrade levels. The first case is if you spread out your units nicely (or you have a sick upgrade advantage which can be the case vs mutas and therefore the bounce attacks together with guardian shield do 0 dmg most of the time), the second case is if you fight it straight up with bunched up units.
For a general rule of thumb about getting +2 armor or +1 shields first you also need to take into account which unit ratio/composition your are using and vs which units/unit composition you are fighting. Otherwise you will just get wrong results. EG.Huk for example always went for fast +2 armor once he spotted muta play, so his stalker groups that were defending all his bases that had no sentries with them due to the sentry-speed resulted in having an armor value of 3 and not getting any glaive bounce dmg on their normal hitpoints (or only 1 dmg each 3 hits from +1 attack mutas ...). He then always proceeded to get up to +3 attack again. If you calculate the dmg taken (also since how many noted already it makes way more difference to go up to 3 armor instead of 2 instead of going up to 1 armor on shields instead of having 0) it's way more beneficial. But then again in a real scenario you mith have a lot of zealots (armor better again) or maybe guardian shield and archons always (so shield much better), or even air unit support or always blinking back hurt stalkers in time (again shields). So in theory if you would not be zealot-heavy and always have guardian shield available at all times, even +3 attack mutas would do no glaive bounce dmg (well nearly no dmg like I stated before, but basically zero ... exaclt the amount they would always take even with +3 armor) on the units, so getting +1 shield is better. Who manages to always get up guardian shield if mutas harass you from different sides? I hardly see pro's having sentries around everywhere and if you just keep one single sentry with some stlakers back, they try to snipe out this lonely sentry. :-)
I hope that people don't make misscalculations again now in this thread and post it without even doing real testing beforehand and missinforming others maybe without even being aware of that themselves.
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Please someone correct me if I'm incorrect, ASSUMPTION: mainly that the last hit of shield "HP" transfers to health:
Just the way my brain works i started to think of how getting 0/1/1(or 0/2/2 or 0/3/3) would affect probes when mutas harras. I only think of this because that is probably the most aggravating thing that happens to me in SC2.
Probe: 20/20
Muta: 9 to first target/ 3 to 2nd target/ 1 to last target (with 0 attack)
No matter what upgrades it would take 3 primary hits to take down the shields of a probe, but with 0/1/1 the probe takes 21 damage so once its shields are gone it is left with 19 hp. But now the shields are gone it takes 8 damage so it needs to be hit 3 more times to die. Without 0/1/1 it takes 27 damage with the first 3 shots leaving it with 13 hp meaning it need to only take 2 shots to kill. So it takes an additional primary hit to kill a probe. With 0/1/1 vs a 0/0 muta it then takes 30 (20 shield hits for 1 damage and 10 health hits for 2 damage) secondary and 40 3rd hits. so this means with 0/1/1 it takes 6 mutas 1/0 to "one shot" a probe. With 1/0 on mutas it takes still takes 3 shots to take down the shields (3 shots for 8 = 24) leaving 16 hp meaning it will take 2 shots of 9 to finish it off. the main benefit of 0/1/1 (in my eyes) are instantly shut down once they get +1 because it then takes 5 shots to kill a probe. So for every shield and armor upgrade it takes it takes an additional muta or and additional attack upgrade to kill a probe.
This also effects cannons/pylons, it takes 38 primary attacks from a muta to kill a cannon with no upgrades on ether. with +1 shields means it takes 41 hits (takes 22 attacks to drain the shields and then 19 attacks to drain the HP). As for pylons normally it takes 50 attacks to kill a pylon. With +1 shields it takes 54 hits (29 hits to drain shields and then 25 hits to kill the health). Also this means with 0/1/1 if probes are hit with secondary attack when mutas are killing pylons it takes then 30 hits to kill a probe instead of 14.
I only wrote this out because of A) boredom and B) i did the math for myself and i figured i would share it with the community.
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If you're concerned with the durability of your stalkers against mutas, somethings horribly wrong. If you aren't massively behind, he's going to be running away from your stalkers, not fighting them head on. That's why it's better to get attack upgrades and storm or archon.
If he IS attacking you head on, the best option is armor upgrades+GS
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On November 16 2011 06:57 Hane wrote:Protoss Shields (S) Upgrades the shields of all Protoss units and structures. Quite good too vs mutaling gogo double forge shield/armor *o*
I think this fact alone makes shields better, maybe even better to get BEFORE armour, when cannons are so crucial in holding off those first set of mutas that number from 8-10, +1 shield armour to cannons can make a huge difference.
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EPT
